No Arabic abstract
The transportation $mathrm{L}^p$ distance, denoted $mathrm{TL}^p$, has been proposed as a generalisation of Wasserstein $mathrm{W}^p$ distances motivated by the property that it can be applied directly to colour or multi-channelled images, as well as multivariate time-series without normalisation or mass constraints. These distances, as with $mathrm{W}^p$, are powerful tools in modelling data with spatial or temporal perturbations. However, their computational cost can make them infeasible to apply to even moderate pattern recognition tasks. We propose line
We prove that functions of locally bounded deformation on $mathbb{R}^n$ are $mathrm{L}^{n/(n-1)}$-differentiable almost everywhere. More generally, we show that this critical $mathrm{L}^p$-differentiability result holds for functions of locally bounded $mathbb{A}$-variation, provided that the first order, homogeneous, linear differential operator $mathbb{A}$ has finite dimensional null-space.
Many problems in science and engineering can be formulated in terms of geometric patterns in high-dimensional spaces. We present high-dimensional convolutional networks (ConvNets) for pattern recognition problems that arise in the context of geometric registration. We first study the effectiveness of convolutional networks in detecting linear subspaces in high-dimensional spaces with up to 32 dimensions: much higher dimensionality than prior applications of ConvNets. We then apply high-dimensional ConvNets to 3D registration under rigid motions and image correspondence estimation. Experiments indicate that our high-dimensional ConvNets outperform prior approaches that relied on deep networks based on global pooling operators.
We study a class of mathematical and statistical algorithms with the aim of establishing a computer-based framework for fast and reliable automatic abnormality detection on landmark represented image templates. Under this framework, we apply a landmark-based algorithm for finding a group average as an estimator that is said to best represent the common features of the group in study. This algorithm extracts information of momentum at each landmark through the process of template matching. If ever converges, the proposed algorithm produces a local coordinate system for each member of the observing group, in terms of the residual momentum. We use a Bayesian approach on the collected residual momentum representations for making inference. For illustration, we apply this framework to a small database of brain images for detecting structure abnormality. The brain structure changes identified by our framework are highly consistent with studies in the literature.
Contour tracking in adverse environments is a challenging problem due to cluttered background, illumination variation, occlusion, and noise, among others. This paper presents a robust contour tracking method by contributing to some of the key issues involved, including (a) a region functional formulation and its optimization; (b) design of a robust and effective feature; and (c) development of an integrated tracking algorithm. First, we formulate a region functional based on robust Earth Movers distance (EMD) with kernel density for distribution modeling, and propose a two-phase method for its optimization. In the first phase, letting the candidate contour be fixed, we express EMD as the transportation problem and solve it by the simplex algorithm. Next, using the theory of shape derivative, we make a perturbation analysis of the contour around the best solution to the transportation problem. This leads to a partial differential equation (PDE) that governs the contour evolution. Second, we design a novel and effective feature for tracking applications. We propose a dimensionality reduction method by tensor decomposition, achieving a low-dimensional description of SIFT features called Tensor-SIFT for characterizing local image region properties. Applicable to both color and gray-level images, Tensor-SIFT is very distinctive, insensitive to illumination changes, and noise. Finally, we develop an integrated algorithm that combines various techniques of the simplex algorithm, narrow-band level set and fast marching algorithms. Particularly, we introduce an inter-frame initialization method and a stopping criterion for the termination of PDE iteration. Experiments in challenging image sequences show that the proposed work has promising performance.
As a unique and promising biometric, video-based gait recognition has broad applications. The key step of this methodology is to learn the walking pattern of individuals, which, however, often suffers challenges to extract the behavioral feature from a sequence directly. Most existing methods just focus on either the appearance or the motion pattern. To overcome these limitations, we propose a sequential convolutional network (SCN) from a novel perspective, where spatiotemporal features can be learned by a basic convolutional backbone. In SCN, behavioral information extractors (BIE) are constructed to comprehend intermediate feature maps in time series through motion templates where the relationship between frames can be analyzed, thereby distilling the information of the walking pattern. Furthermore, a multi-frame aggregator in SCN performs feature integration on a sequence whose length is uncertain, via a mobile 3D convolutional layer. To demonstrate the effectiveness, experiments have been conducted on two popular public benchmarks, CASIA-B and OU-MVLP, and our approach is demonstrated superior performance, comparing with the state-of-art methods.